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Jackie has two solutions that are 2% sulphuric acid and 12% sulphuric acid by volume respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of solution that is 5% sulphuric acid, approximately how many liters of 2% solution will be present?

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300

420

answer is D.

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Detailed Solution

Concept- We will be using formula,
amount of sulphuric acid by volume

= \frac{volume of the solution \times percentage of sulphuric acid}{100}

Let the solution of 2% of sulphuric acid by volume be

S_{1}

, and the solution of 12% of sulphuric acid by volume be

S_{2}

.
Given i.e, in the final solution 5% of sulphuric acid by volume is present.
Final solution =

k liters

S_{1}

+ (

(60 + k)

liters

S_{2})

amount of sulphuric acid by volume

= \frac{volume of the solution \times percentage of sulphuric acid}{100}

\Rightarrow

amount of sulphuric acid by volume

= \frac{60 \times 5}{100}

\Rightarrow

amount of sulphuric acid by volume

=

3 liters…………(i)
Now,
solution

S_{1}

of 2% of sulphuric acid by volume =

\frac{volume of the solution s_{1} \times percentage of sulphuric acid in solution s_{1}}{100}

\Rightarrow solution S_{1} of 2 % of sulphuric acid by volume = \frac{2 k}{100}

……..(ii)
Again,
solution

S_{2}

of 2% of sulphuric acid by volume =

\frac{volume of the solution s_{2} \times percentage of sulphuric acid in solution s_{2}}{100}

\Rightarrow

solution

S_{2}

of 2% of sulphuric acid by volume =

\frac{(60 - k) \times 12}{100}

……….(iii)
Amount of sulphuric acid in the final solution by volume

=

Solution of 2% of sulphuric acid by volume be

S_{1}

+Solution of 12% of sulphuric acid by volume be

S_{2}

………(iv)
On substituting equations (i),(ii),(iii),(iv), we get

\Rightarrow 3 = \frac{2 k}{100} + 12 (\frac{60 - k}{100})

\Rightarrow 3 = \frac{720 + 10 k}{100}

\Rightarrow 300 = 720 + 10 k

\Rightarrow 420 = 10 k

\Rightarrow k = 42

So, 42 liters of the 2% sulphuric acid by volume is contained in the final solution.
Hence, the correct answer is option 4.

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Jackie has two solutions that are 2% sulphuric acid and 12% sulphuric acid by volume respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of solution that is 5% sulphuric acid, approximately how many liters of 2% solution will be present?

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